论文标题
基于测量的量子计算的资源层次结构
Hierarchies of resources for measurement-based quantum computation
论文作者
论文摘要
对于某些受限制的计算任务，量子力学比任何可能的经典实现都提供了可证明的优势。这些结果中的几个已通过基于测量的量子计算（MBQC）的框架证明，其中非本地性和更常见的上下文性被确定为某些量子计算的必要资源。在这里，我们通过在允许的操作和可访问的Qubits数量上完善其资源要求，从而更详细地考虑MBQC的计算能力。更确切地说，我们确定可以在非自适应MBQC中计算哪些布尔函数，其本地操作包含在Clifford层次结构中的有限级别内。此外，对于限制了某些子理论（例如稳定器MBQC）的非自适应MBQC，我们计算计算给定布尔函数所需的量子数量最少。我们的结果表明，资源的层次结构更为敏锐地描述了MBQC的力量，而不是上下文性与非上下文性的二进制。
For certain restricted computational tasks, quantum mechanics provides a provable advantage over any possible classical implementation. Several of these results have been proven using the framework of measurement-based quantum computation (MBQC), where non-locality and more generally contextuality have been identified as necessary resources for certain quantum computations. Here, we consider the computational power of MBQC in more detail by refining its resource requirements, both on the allowed operations and the number of accessible qubits. More precisely, we identify which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy. Moreover, for non-adaptive MBQC restricted to certain subtheories such as stabiliser MBQC, we compute the minimal number of qubits required to compute a given Boolean function. Our results point towards hierarchies of resources that more sharply characterise the power of MBQC beyond the binary of contextuality vs non-contextuality.
